Model-based segmentation has numerous applications in interventions and follow-up studies, for instance in radiation therapy planning Deformable models, described by flexible surface meshes, for instance triangle meshes, are adapted to the corresponding image structures. Usually this adaptation is carried out for every object separately by optimizing a weighted sum of two competing energies: an external energy driving the mesh triangles towards features in the image, and an internal energy preserving the form of the model. An implementation of this method is described by J. Weese, M. Kaus, C. Lorenz, S. Lobregt, R. Truyen, V. Pekar in “Shape constrained deformable models for 3D medical Image segmentation”, IPMI 2001, 380-387, hereinafter referred to as Ref. 1.
A separate adaptation of multiple meshes cannot take spatial relations between several objects into account and hence often results in wrong adaptation results such as for instance intersecting meshes. A first attempt to overcome this problem is described in WO 2004/010374 A2 “Simultaneous segmentation of multiple or composed objects by mesh adaptation”. There, additional edges connecting two meshes are introduced into the model. These additional edges are considered as degenerated triangles, and the internal energy is extended for these triangles in order to keep the spatial relationship of the two meshes. However, this procedure is only applicable when the spatial relationship of two objects can be described by pre-positioning the corresponding meshes, since the lengths and positions of the additional edges or triangles are to be preserved. But in a lot of medical applications inner organs are involved which can slide with respect to each other, for instance the organs in the abdominal region, the lung with respect to the rib cage, or two successive vertebrae in the spine. For such organs simultaneous segmentation with the method described in WO 2004/010374 A2 can only avoid mesh intersection if the meshes are correctly pre-positioned, but will nevertheless result in an adaptation with wrong spatial relationships.